Question: $-3ef + eg - 8e - 1 = 5f - 5$ Solve for $e$.
Combine constant terms on the right. $-3ef + eg - 8e - {1} = 5f - {5}$ $-3ef + eg - 8e = 5f - {4}$ Notice that all the terms on the left-hand side of the equation have $e$ in them. $-3{e}f + 1{e}g - 8{e} = 5f - 4$ Factor out the $e$ ${e} \cdot \left( -3f + g - 8 \right) = 5f - 4$ Isolate the $e$ $e \cdot \left( -{3f + g - 8} \right) = 5f - 4$ $e = \dfrac{ 5f - 4 }{ -{3f + g - 8} }$ We can simplify this by multiplying the top and bottom by $-1$. $e= \dfrac{-5f + 4}{3f - g + 8}$